Under the action of a strong earthquake, dynamic damages, such as the pullout of the inner anchor section and the abruption of the anchor cable, are induced by the prestressed anchor cable frame. A novel anti-seismic measure involves setting springs at the outer anchor head, and an important design parameter is the spring stiffness. The seismic responses of slope under various PGAs and seismic waves with different durations were studied using a three-dimensional numerical model of bedrock-overburden slope reinforced by a prestressed anchor cable frame with springs at the anchor head. A method for determining the reasonable stiffness of spring components was proposed to control the displacement of the slope and reduce the load on the anchor cable. Results show that the damping effect gradually emerges with a decrease in spring stiffness. The horizontal acceleration at the top of the slope is slightly affected by the stiffness change. However, the slope displacement and spring deformation sharply increase when the spring stiffness is lower than the critical value. The minimum stiffness is determined by taking the empirical limit of slope permanent displacement as the primary control condition and combining the “straight-curved boundary point” of the fitting curve of spring peak stroke and stiffness. The permanent displacement of 10 cm and delimit curvature k less than 0.002k_max are taken for the calculation model to obtain a reasonable range of spring stiffness, i.e., (2.5, 3.8) kN/mm, under 0.4g-0.6g. The proposed method can provide a reference for the seismic design of prestressed anchorage engineering of slopes.